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What is the number of terms in the arithmetic progression 1, 4, 7, ... needed to achieve a sum of 1001?
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Solution: Step 1: The sum of n terms of an A.P., Sn = n/2 * [2a + (n-1)d] Step 2: Given Sn = 1001, a = 1, d = 3 Step 3: Substitute values: 1001 = n/2 * [2*1 + (n-1)*3] Step 4: Simplify: 2002 = 3n^2 - n Step 5: Rearrange: 3n^2 - n - 2002 = 0 Step 6: Solve quadratic equation: n = 26
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